Coronary artery disease is a common ailment that affects millions of people. Coronary artery disease may cause the blood vessels providing blood to the heart to develop lesions, such as a stenosis (abnormal narrowing of a blood vessel). As a result, blood flow to the heart may be restricted. Significant strides have been made in the treatment of coronary artery disease including both medical therapy (e.g. statins) or surgical alternatives (e.g., percutaneous coronary intervention (PCI) and coronary artery bypass graft surgery (CABG)). Invasive assessments are commonly used to assess the type of treatment a patient may receive. However, indirect or noninvasive assessments for formulating a patient treatment are being explored and developed.
Heart disease is typically viewed as resulting from vessel disease, in particular, narrowing or blockage inside vessel lumens in a way that impacts blood flow. Patient-specific modeling of blood flow in the circulation may include three or more elements: first, a description of the anatomic region of interest; second, the mathematical “governing equations” enumerating the physical laws of blood flow within the region of interest; and, third, “boundary conditions” to define physiologic relationships between variables at the boundaries of the region of interest. While the anatomic region of interest and the boundary conditions may be unique to each patient and the specific vascular territory, the governing equations describing velocity and pressure may be universal and apply in different patients and other arterial beds.
Three-dimensional models of blood flow may employ numerical methods to solve the Navier-Stokes equations governing fluid dynamics. In the last 25 years, three-dimensional numerical methods have become a standard approach for simulating blood flow in arteries. One technique includes simulating blood flow in patient-specific models derived from medical imaging data, combining three-dimensional models of blood flow in the large arteries with one-dimensional and lumped parameter models of arteries upstream or downstream of the regions of interest, and solving the coupled problems of blood flow and vessel wall dynamics. This coupling between three-dimensional models and reduced order models enable the solution of realistic coronary artery flow and pressure waveforms.
The ability to quantify blood flow in the human coronary arteries using image-based, patient-specific modeling has enabled the noninvasive quantification of fractional flow reserve (FFR). FFR may be defined by the ratio of maximal hyperemic flow to part of the myocardium in the presence of coronary artery disease to the maximum hyperemic flow to the same myocardial territory in the hypothetical case where the supplying vessels are normal. Clinically, FFR is measured invasively using a pressure-wire inserted into the coronary artery during cardiac catheterization by the ratio of distal perfusion pressure to aortic pressure under conditions of pharmacologically-induced maximum hyperemia. FFR can uniquely identify epicardial obstructive disease that is limiting hyperemic flow and may be correctable by percutaneous coronary intervention (PCI). A recommended threshold separating a positive from a negative FFR may be a predetermined value of 0.80, i.e. when the distal coronary pressure is 80% of the aortic pressure under conditions of maximal hyperemia. Deferral of PCI for vessels with an FFR >0.80 may improve clinical outcomes and reduce costs compared to angiography guided intervention. PCI in vessels with a measured FFR ≤0.80 may reduce the combined end-point of death, myocardial infarction, and urgent revascularization as compared to optimal medical therapy. Current guidelines on myocardial revascularization assign a class I-A recommendation to FFR for the assessment of coronary artery stenoses with a diameter reduction ranging from 50 to 90% unless there is non-invasive proof of ischemia. There is a strong motivation to obtain FFR data noninvasively to determine which patients to refer to, or defer from, cardiac catheterization. Since FFR cannot be directly measured noninvasively, it is necessary to identify a surrogate that can be determined and which correlates with invasive FFR.
While evidence for the clinical benefit of fractional flow reserve is substantial, invasive determination of FFR can be expensive and not free of complications. Hence, there is a strong motivation to obtain this data noninvasively to determine which patients to refer to, or defer from, cardiac catheterization. Due to difficulties in noninvasive measurement of coronary artery blood pressure and flow, and in direct measurement of FFR, it has become advantageous to identify a surrogate that can be determined and which correlates with invasive FFR.
One method to noninvasively determine FFR is the simulation of coronary hemodynamics using computational fluid dynamics based on coronary artery anatomy as determined by FFR computed tomography (FFRCT). FFRCT has emerged as a viable alternative to anatomic or physiologic surrogates for invasively-measured FFR. FFRCT technology uses computational fluid dynamics to quantify the ratio of coronary artery to aortic pressure under conditions of simulated maximal hyperemia in a patient-specific anatomic and physiologic model derived from coronary CT angiography data and established biologic principles relating form (anatomy) to function (physiology). The diagnostic performance of FFRCT has been evaluated in three prospective, multicenter clinical trials in over 600 patients and more than 1000 vessels using FFR as the reference standard. In each study, FFRCT showed good correlation to FFR and demonstrated significant improvement in diagnostic accuracy and specificity, without sacrificing sensitivity, compared to anatomic assessment by coronary CT angiography alone.
However, the current correlation between FFRCT and measured FFR has room for improvement. One potential means to improve this technology would be to improve the estimation of coronary boundary conditions which define physiologic relationships between variables at the boundaries of the region of interest. These boundary conditions may encode flow, pressure, or a relationship between pressure and flow, such as impedance or resistance. In some implementations, the boundary conditions may be derived using form-function relationships from the CT anatomic data. A means to estimate these boundary conditions using other data available in the images would be highly advantageous. One potential approach that has been proposed to derive flow data from CT images is Transluminal Attenuation Flow Encoding (TAFE) where flow rate is inferred from gradients of contrast intensity along the length of the vessel and information about the time-dependent changes in the arterial contrast. A shortcoming of the TAFE approach is that it relies on a significant idealization of the coronary artery geometry and simplistic transport models. For example, the TAFE method involves the assumption that the ratio of flow to area does not change significantly along the length of the vessel, which would be violated in coronary artery stenoses where flow is constant but area changes significantly. Thus, while this approach has demonstrated promise in animal models, its utility in computing blood flow in patients is unproven. Performance has also been demonstrated only on single isolated lesions, and with either serial lesions or models with competing lesions in two branching vessels, the boundary condition approximation is/may not be valid. Further, the assumption of maximum dispersion occurring at outlets can be inaccurate depending on imaging resolution relative to outlet size and extent of disease burden. Thus, there is a desire for a system for quantification of blood that improves the estimation of coronary boundary conditions which define physiologic relationships between variables at the boundaries of the region of interest.